New exact travelling waves solutions to the combined KDV-MKDV and generalized Zakharov equations

Abstract

In this paper, the solutions of a first-order nonlinear ordinary differential equation with a sixth-degree nonlinear term and Fan's direct algebraic method of obtaining exact solution to nonlinear PDEs are applied to two nonlinear evolution equations, the combined KdV-MKdV equation and generalized Zakharov equations. As a result, some special exact travelling wave solutions are obtained which include new bell and kink profile solitary wave solutions, bright and dark solitary wave solutions, triangular periodic wave solutions and singular solutions.